A method for manufacturing a weft knit fabric with knitting with a double border closed transversely at least one of its ends or at an intermediate region thereof with a knitting machine for knitting with reciprocating motion and a fabric obtained with the method. The method comprises: an initial knitting step (F1), in which the needles arranged in a sector (A) of the needle holder are moved to knit at a feed or drop in order to form knitting; a central knitting step (FC), in which the needle holder is actuated with a reciprocating motion with respect to the feed and in which the needles of the sector (A) are divided, according to a preset selection, into active needles, which can be moved to knit at the feed, alternated with inactive needles, which remain excluded from knitting at the feed during the central knitting step (FC), retaining in their tip or head the last loop of knitting formed during the initial knitting step (F1). The central knitting step (FC) comprises: a first fraction (FC1), in which the active needles located in a first region (A1) of the sector (A) are actuated to knit at the feed and form knitting and the active needles located in at least one second region (A2) of the sector (A), which is contiguous or adjacent to the first region (A1), are moved progressively to knit at the feed starting from the end of the second region (A2) that borders the first region (A1) and increasing progressively the number of active needles of the second region (A2) moved to knit at the feed at each at least one cycle, composed of a forward motion and a return motion, of the reciprocating motion of the needle holder with respect to the feed; a second fraction (FC2) of the central knitting step (FC), in which the active needles located in the first region (A1) of the sector (A) are actuated to knit at the feed and form knitting as in the first fraction (FC1) of the central knitting step (FC) and the active needles located in the second region (A2) of the sector (A) are excluded progressively from knitting at the feed, starting from the end of the second region (A2) that lies opposite the first region (A1) and decreasing progressively the number of active needles of the second region (A2) that are moved to knit at the feed at each at least one cycle, composed of a forward motion and a return motion, of the reciprocating motion of said needle holder with respect to the feed, retaining in their tip or head the last formed loop of knitting. Then, in a final knitting step (FF), knitting with all the needles of the sector (A) is resumed.